Belt for continuously variable transmission

ABSTRACT

In a belt for a continuously variable transmission including a large number of metal elements carried on metal ring assemblies each of which is comprised of a plurality of endless metal rings laminated one on another, the amplitude σa 1  of a total stress on the inner circumferential surface of the innermost metal ring is larger than the amplitude σa n  of a total stress on the inner circumferential surfaces of the other metal rings, and a maximum value of a tensile stress on the inner circumferential surface of the innermost metal ring is larger than a maximum value of a tensile stress on the inner circumferential surfaces of the other metal rings. Therefore, a compressive residual stress is applied to the inner circumferential surface of the innermost metal ring used under the severest condition, and the middle value σm 1  of the amplitude σa 1  of the stress on the innermost metal ring is brought close or equal to 0. Thus, the middle value of the stress on the inner circumferential surface of the innermost metal ring which is most liable to be broken can be brought close to 0, thereby enhancing the durability of the entire metal ring assembly.

FIELD OF THE INVENTION

The present invention relates to a belt for a continuously variabletransmission including a large number of metal elements carried on metalring assemblies each of which is comprised of a plurality of endlessmetal rings laminated one on another.

BACKGROUND ART

When a metal belt of a continuously variable transmission is clamped inV-faces of a drive pulley and a driven pulley, a tension is generated inthe metal belt. This tension is varied by a driving force and a brakingforce received from both the pulleys and for this reason, the tensilestress on each of the metal rings is varied periodically with travelingof the metal belt. The traveling metal belt is bent at a pulley-woundzone and drawn out in a chord portion between the pulleys and hence, abending stress on each metal ring is also varied periodically. As aresult, a total stress (a sum of the tensile stress and the bendingstress) applied to each of the metal rings is varied periodically withone rotation of the metal belt being as one cycle.

A belt for a continuously variable transmission has been proposed inJapanese Patent Application Laid-open No. 57-57938, in which acompressive residual stress is applied to an outer circumferentialsurface of each of the metal rings of a metal ring assembly, and atensile residual stress is applied to an inner circumferential surfaceof the metal ring, whereby the middle value of the amplitude of theperiodically varied stress (the middle value of the stress) on each ofmetal rings is brought as close to 0 as possible to prolong the fatiguelife.

The innermost metal ring of such metal ring assembly abuts against asaddle surface of the metal element, while the inner circumferentialsurfaces of the metal rings other than the innermost metal ring abutagainst the outer circumferential surfaces of the other metal rings,respectively, and hence, friction coefficients of abutment portions ofthe innermost one and the other metal rings are of different values.Specifically, it has been ascertained by the actual measurement that afriction coefficient of the inner circumferential surface of theinnermost metal ring abutting against the saddle surface of the metalelement is larger than a friction coefficient of the innercircumferential surface of the metal ring other than the innermost metalring. As a result, as will be described in detail in connection with anembodiment hereinafter, the amount of variation in tension of theinnermost metal ring (a difference between the maximum and minimumvalues of a tension in one cycle) is larger than the amount of variationin tension of the other metal rings.

In the above conventional belt, however, the compressive residual stressis applied to the outer circumferential surfaces of all the metal ringsand the tensile residual stress is applied to the inner circumferentialsurfaces of all the metal rings, without discrimination between theinnermost metal ring and the other metal rings. Therefore, there is aproblem that the durability of the entire metal belt is limited by thedurability of the innermost metal ring used under a severe conditionwith a large amount of variation in tension. The point of start of theactual breakage is on the inner circumferential surface of the innermostmetal ring and for this reason, an attention must be paid to theamplitude σa and middle value cm of the stress on the innercircumferential surface of the metal ring rather than the outercircumferential surface. The middle value σm of the stress is positive(tension) and hence, there is a problem that if the tensile residualstress is applied to the inner circumferential surface of the metalring, the middle value σm of the stress is increased, resulting in areduced life.

DISCLOSURE OF THE INVENTION

The present invention has been accomplished with the above circumstancesin view, and it is an object of the present invention to prolong thefatigue life of the inner circumferential surface of the innermost metalring which is most liable to be broken, thereby enhancing the durabilityof the entire metal ring assembly.

To achieve the above object, according to the present invention, thereis provided a belt for a continuously variable transmission, comprisinga large number of metal elements carried on metal ring assemblies eachof which is comprised of a plurality of endless metal rings laminatedone on another, characterized in that a compressive residual stress isapplied to at least an inner circumferential surface of an innermost oneof the metal rings which is in contact with a saddle surface of themetal element, the compressive residual stress applied to the innermostmetal ring being larger than a compressive residual stress applied tothe metal rings other than the innermost metal ring.

In addition to the above arrangement, there is provided a belt for acontinuously variable transmission, wherein the compressive residualstress is applied to at least the inner circumferential surface of theinnermost metal ring, so that a fatigue life defined by an amplitude σa₁and a middle value σm₁ of a stress on the inner circumferential surfaceof the innermost metal ring is equal to a fatigue life defined by anamplitude σa_(n) and a middle vale σm_(n) of a stress on the innercircumferential surfaces of the metal rings other than the innermostmetal ring.

The function and effect according to the present invention are asfollows.

The friction coefficient of the inner circumferential surface of theinnermost metal ring which is in contact with the saddle surface of themetal element is larger than the friction coefficient between the metalrings which are in contact with one another and hence, the amount ofvariation in tension on the innermost metal ring is larger than theamount of variation in tension on the other metal rings, and theamplitude of the stress on the innermost metal ring attendant on thevariation in tension is larger than the amplitude of the stress on theother metal rings. As a result, when the total stress resulting from theaddition of the bending stress on the metal ring to the tensile stresson the metal ring is considered, the amplitude of the total stress onthe inner circumferential surface of the innermost metal ring is largerthan the amplitude of the total stress on the inner circumferentialsurfaces of the other metal rings, and the middle value of the stress onthe inner circumferential surface of the innermost metal ring is largerthan the middle value of stress on the inner circumferential surfaces ofthe other metal rings.

Therefore, the compressive residual stress is applied to the innercircumferential surface of the innermost metal ring used under theseverest condition, and the middle value of the amplitude of the stresson the innermost metal ring is brought close to or equal to 0 (zero).Thus, the difference between the maximum value of the tensile stress andthe maximum value of the compressive stress applied to the innercircumferential surface of the innermost metal ring can be decreased toenhance the durability of the innermost metal ring, thereby prolongingthe life of the entire metal ring assembly.

Particularly, by setting the value of the compressive residual stresssuch that the fatigue life of the innermost metal ring is equal to thefatigue life of the other metal rings, the life of the entire metal ringassembly can be prolonged most effectively.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 to 10 show an embodiment of the present invention. FIG. 1 is askeleton illustration of a power transmitting system of a vehicle havinga continuously variable transmission mounted thereon; FIG. 2 is apartial perspective view of a metal belt; FIG. 3 is a view forexplaining a tensile stress applied to a metal ring; FIG. 4 is a diagramshowing the balance of a force applied to the metal ring; FIG. 5 is agraph showing a variation in ΔT₁/ΔT_(ALL) with respect to a frictioncoefficient ratio ξ; FIGS. 6A and 6B are diagrams explaining the shapesof the metal ring in a free state and in a service state; FIG. 7 is agraph showing a variation in the tensile stress applied to an innercircumferential surface of the metal ring; FIG. 8 is a graph showing avariation in a bending stress applied to the inner circumferentialsurface of the metal ring; FIG. 9 is a graph showing a variation intotal stress applied to the inner circumferential surface of the metalring; and FIG. 10 is a graph showing equi-life lines of the metal ring.

BEST MODE FOR CARRYING OUT THE INVENTION

The embodiment of the present invention will now be described withreference to the accompanying drawings.

FIG. 1 shows the skeleton structure of a metal belt-type continuouslyvariable transmission T mounted on an automobile. An input shaft 3 isconnected to a crankshaft 1 of an engine E through a damper 2 and alsoconnected to a drive shaft 5 of the metal belt-type continuouslyvariable transmission T through a starting clutch 4. A. drive pulley 6is mounted on the drive shaft 5 and includes a stationary pulley half 7secured to the drive shaft 5, and a movable pulley half 8 which ismovable toward and away from the stationary pulley half 7. The movablepulley half 8 is biased toward the stationary pulley half 7 by ahydraulic pressure applied to an oil chamber 9.

A driven pulley 11 is mounted on a driven shaft 10 disposed in parallelto the drive shaft 5, and includes a stationary pulley half 12 securedto the driven shaft 10, and a movable pulley half 13 which is movabletoward and away from the stationary pulley half 12. The movable pulleyhalf 13 is biased toward the stationary pulley half 12 by a hydraulicpressure applied to an oil chamber 14. A metal belt 15 comprising alarge number of metal elements 32 supported on a pair of left and rightmetal ring assemblies 31, 31 is wound around the drive pulley 6 and thedriven pulley 11 (see FIG. 2). Each of the metal ring assemblies 31comprises twelve metal rings 33 laminated one on another.

A forward drive gear 16 and a backward drive gear 17 are rotatablycarried on the driven shaft 10 and are capable of being selectivelycoupled to the driven shaft 10 by a selector 18. Secured to an outputshaft 19 disposed in parallel to the driven shaft 10 are a forwarddriven gear 20 meshed with the forward drive gear 16, and a backwarddriven gear 22 meshed with the backward drive gear 17 through a backwardidle gear 21.

The rotation of the output shaft 19 is inputted to a differential 25through a final drive gear 23 and a final driven gear 24 and thentransmitted from the differential 25 through left and right axles 26, 26to driven wheels W, W.

A driving force from the engine E is transmitted through the crankshaft1, the damper 2, the input shaft 3, the starting clutch 4, the driveshaft 5, the drive pulley 6, the metal belt 15 and the driven pulley 11to the driven shaft 10. When a forward travel range is selected, thedriving force of the driven shaft 10 is transmitted through the forwarddrive gear 16 and the forward driven gear 20 to the output shaft 19 tomove the vehicle forwards. When a backward travel range is selected, thedriving force of the driven shaft 10 is transmitted through the backwarddrive gear 17, the backward idle gear 21 and the backward driven gear 22to the output shaft 19 to move the vehicle backwards.

In this case, the shift ratio is continuously regulated by controllingthe hydraulic pressure applied to the oil chamber 9 in the drive pulley6 and the oil chamber 14 in the driven pulley 11 in the metal belt-typecontinuously variable transmission T by a hydraulic pressure controlunit U₂ which is operated by the command from an electronic control unitU₁. More specifically, if the hydraulic pressure applied to the oilchamber 14 in the driven pulley 11 is increased relative to thehydraulic pressure applied to the oil chamber 9 in the drive pulley 6,the groove width of the driven pulley 11 is decreased, leading to anincreased effective radius. According to this, the groove width of thedrive pulley 6 is increased, leading to a decreased effective radius.Therefore, the shift ratio of the metal belt-type continuously variabletransmission T is continuously varied toward “LOW”. Reversely, if thehydraulic pressure applied to the oil chamber 9 in the drive pulley 6 isincreased relative to the hydraulic pressure applied to the oil chamber14 in the driven pulley 11, the groove width of the drive pulley 6 isdecreased, leading to an increased effective radius. According to this,the groove width of the driven pulley 11 is increased, leading to adecreased effective radius. Therefore, the shift ratio of the metalbelt-type continuously variable transmission T is continuously variedtoward “TOP”.

FIG. 3 shows a state in which the effective radius of the drive pulley 6is larger than that of the driven pulley 11 with the vehicle being in astate in which it is traveling at the highest speed (TOP state). Thethickness of the metal belt 15 in FIG. 3 diagrammatically represents themagnitude of the tensile stress applied to each of the metal rings 33due to the tension of the metal belt 15. In a returning-side chordportion (a region A) in which the metal belt 15 is returned from thedriven pulley 11 to the drive pulley 6, such stress is of a given valueσT_(LOW), and in an advancing-side chord portion (a region C) in whichthe metal belt 15 is delivered from the drive pulley 6 to the drivenpulley 11, such stress is of a given value σT_(HIGH). The stressσT_(LOW) in the region A is smaller than the stress σT_(HIGH) in theregion C. In a section (a region B) in which the metal belt 15 is woundaround the drive pulley 6, the stress is increased from the valueσT_(LOW) to the value σT_(HIGH) from the inlet side to the outlet side.In a section (a region D) in which the metal belt 15 is wound around thedriven pulley 11, the stress is decreased from the value σT_(HIGH) tothe value σT_(LOW) from the inlet side to the outlet side.

The tension of the metal belt 15 is equally shared by the pair of metalring assemblies 31, 31, and the tension of each of the metal ringassemblies 31 is shared by the twelve metal rings 33 constituting themetal ring assembly 31. In this case, the stresses of the eleven metalrings 33 second to twelfth from the inside, excluding the innermostmetal ring 33 which is in contact with a saddle surface 32 ₁ of themetal element 32, are equal to one another, but the stress of theinnermost metal ring 33 assumes a value different from the stresses ofthe second to twelfth metal rings 33. The reason will be described belowwith reference to FIG. 4.

First, a case where the metal ring assembly comprises three metal ringswill be considered as a simple model. If a vertical drag acting betweenthe outermost, third ring and the inner, second ring in a pulley-woundzone is represented by N, a vertical drag acting between the second ringand the first ring is equal to 2N, and a vertical drag acting betweenthe first ring and the saddle surface of the metal element is equal to3N. Here, if a friction coefficient between the metal rings which are incontact with each other (which will be referred to as a ring-ringfriction coefficient hereinafter) is represented by μ_(ss); a frictioncoefficient between the metal ring and the metal element (which will bereferred to as a ring-element friction coefficient hereinafter) isrepresented by μ_(s); and loads of the first, second and third rings arerepresented by F₁, F₂ and F₃, respectively, amounts ΔT₁, ΔT₂ and ΔT₃ ofvariation in tension on the metal rings are given according to thefollowing equations (1), (2) and (3):

ΔT ₃ =F ₃=μ_(ss) N  (1)

ΔT ₂ =F ₂ −F ₃=2μ_(ss) N−μ _(ss) Nμ _(ss) N  (2)

ΔT ₁ =F ₁ −F ₂=3μ_(s) N−2μ_(ss) N  (3)

Namely, the amounts ΔT₂ and ΔT₃ of variation in tension on the secondand third rings having the equal friction coefficients μ_(ss) of theirinner circumferential surfaces are equal to μ_(ss)N, but the amount ΔT₁of variation in tension acting on the first ring having the frictioncoefficients of its inner circumferential surface equal to μ_(s) isequal to 3μ_(s)N−2μ_(ss)N which is different from the amounts ΔT₂ andΔT₃.

The ratio of ΔT₁ to ΔT₂ is given by

ΔT ₁ /ΔT ₂=(3μ_(s) N−2μ_(ss) N)/μ_(ss) N  (4)

and if this equation (4) is extended to a case where the number oflaminated metal rings is n, the following equation is given:

 ΔT ₁ /ΔT ₂ ={nμ _(s)−(n−1)μ_(ss)}/μ_(ss)  (5)

Here, a friction coefficient ratio which is a ratio of the ring-elementfriction coefficient μ_(s) to the ring-ring friction coefficient μ_(ss)is represented by ξ (=μ_(s)/μ_(ss)), the equation (5) can be rewrittenas follows:

ΔT ₁ /ΔT ₂ =nξ−(n−1)=n(ξ−1)+1  (6)

The sum total ΔT_(ALL) of the amounts ΔT₁ to ΔT_(n) of variation intension on the n sheets of metal rings constituting a metal ringassembly is given by $\begin{matrix}\begin{matrix}{{\Delta \quad T_{ALL}} = \quad {{\Delta \quad T_{1}} + {\Delta \quad T_{2}} + \cdots + {\Delta \quad T_{12}}}} \\{= \quad {{\left( {n - 1} \right)\Delta \quad T_{2}} + {\Delta \quad T_{1}}}} \\{= \quad {{\left( {n - 1} \right)\Delta \quad T_{2}} + {\left\{ {{n\left( {\xi - 1} \right)} + 1} \right\} \Delta \quad T_{2}}}} \\{= \quad {n\quad {\xi\Delta}\quad T_{2}}}\end{matrix} & (7)\end{matrix}$

and therefore, if ΔT₂ is eliminated from the equations (6) and (7), thefollowing equation is given:

ΔT ₁ /ΔT _(ALL) ={n(ξ−1)+1}/nξ  (8)

The equation (8) indicates that if the number n of the laminated metalrings included in the metal ring assembly is determined, and thefriction coefficient ratio ξ which is the ratio of the ring-elementfriction coefficient μ_(s) to the ring-ring friction coefficient μ_(ss)is determined, the ratio of the amount ΔT₁ of variation in tension onthe innermost metal ring to the amount ΔT_(ALL) of variation in tensionon the entire metal ring assembly is determined.

The graph in FIG. 5 shows the result of the calculation of the valueΔT₁/ΔT_(ALL) about various friction coefficients ξ in a case where themetal ring assembly is constituted of twelve metal rings (i.e., n=12).The past experience and the actual measurement result show that if ringsidentical to the innermost metal ring are employed as the other metalrings, the ring-element friction coefficient μ_(s) is a value largerthan the ring-ring friction coefficient μ_(ss) and hence, the frictioncoefficient ratio ξ=μ_(s)/μ_(ss) is larger than 1.0.

Supposing that the ring-ring friction coefficient μ_(ss) and thering-element friction coefficient μ_(s) are equal to each other, thefriction coefficient ratio ξ is equal to 1.0, and ΔT₁/ΔT_(ALL) is equalto 0.08. Thus, the innermost metal ring bears the same amount ofvariation in tension as any of the other eleven metal rings, i.e., about8% which is one twelfth of the total sum ΔT_(ALL) of the amounts ofvariation in tension on the entire metal ring assembly. In practice,however, the friction coefficient ratio ξ assumes a value larger than1.0 and for this reason, the amount ΔT₁ of variation in tension on theinnermost metal ring is larger than the amount ΔT_(n) (which is constantabout the eleven metal rings) of variation in tension on any of theother eleven metal rings.

The graph in FIG. 7 shows the variation in tensile stress σT₁ on theinnermost metal ring and the variation in tensile stress σT_(n) on eachof the other eleven metal rings, when the vehicle is in thehighest-speed traveling state described with reference to FIG. 3. Atwo-dot dashed line in FIG. 7 indicates the variation in tensile stressσT₁ on the innermost metal ring, and a one-dot dashed line indicates thevariation in tensile stress σT_(n) on each of the other eleven metalrings other than the innermost metal ring. Due to the discord betweenthe ring-element friction coefficient μ_(s) and the ring-ring frictioncoefficient μ_(ss) described above, the amount ΔT₁ of variation intension on the innermost metal ring (namely, the amount ΔσT₁ ofvariation in stress) is larger than the amount ΔT_(n) of variation intension on any of the other metal rings (namely, the amount σT_(1−LOW)of variation in stress); the minimum tensile stress σT_(1−LOW) of theinnermost metal ring in the returning-side chord portion (the region A)is smaller than the minimum tensile stress σT_(n−LOW) on the other metalrings, and the maximum tensile stress σT_(1−HIGH) of the innermost metalring in the advancing-side chord portion (the region C) is larger thanthe maximum tensile stress σT_(n−HIGH) on the other metal rings.

A tensile stress and a compressive stress based on the bending of themetal ring are applied to the metal ring in addition to the tensilestress based on the tension. As shown in FIGS. 6A and 6B, the metal ringin a free state is circular, but the metal ring in a service state isdeformed into a shape having the regions A, B, C and D. In thereturning-side chord portion (the region A) and in the advancing-sidechord portion (the region C), a radius of curvature which is R₀ in thefree state is increased infinitely (∞). In the region B in which themetal belt is wound around the large-diameter drive pulley, the radiusof curvature which is R₀ in the free state is decreased to R_(DR). Inthe region D in which the metal belt is wound around the small-diameterdriven pulley, the radius of curvature which is R₀ in the free state isdecreased to R_(DN).

In the regions A and C in which the radius of curvature of the metalring is increased, a tensile bending stress is applied to the innercircumferential surface of the metal ring, and a compressive bendingstress is applied to the outer circumferential surface of the metalring. On the other hand, in the regions B and D in which the radius ofcurvature of the metal ring is decreased, a compressive bending stressis applied to the inner circumferential surface of the metal ring, and atensile bending stress is applied to the outer circumferential surfaceof the metal ring. Each of the compressive bending stress and thetensile bending stress is of the same value in the innermost metal ringand the other metal rings.

The graph in FIG. 8 shows the bending stresses applied to the innercircumferential surfaces of the twelve metal rings, when the vehicle isin the highest-speed traveling state described with reference to FIG. 3.As can be seen from FIG. 8, a tensile bending stress σV_(ST) which isconstant in the two chord portions (the regions A and C) is applied tothe inner circumferential surface of each of the metal rings. In theregion B in which the metal belt is wound around the drive pulley havingthe larger radius of curvature, a relatively small compressive bendingstress σV_(DR) is applied to the inner circumferential surface of eachof the metal rings. In the region D in which the metal belt is woundaround the driven pulley having the smaller radius of curvature, arelatively large compressive bending stress σV_(DN) is applied to theinner circumferential surface of each of the metal rings.

The graph in FIG. 9 shows a total stress resulting from the addition oftwo stresses: (1) the stress shown in FIG. 7 and applied to the metalring based on the tension of the metal ring and (2) the stress shown inFIG. 8 and applied to the inner circumferential surface of the metalring based on the bending of the metal ring. In FIG. 9, a bold dashedline indicates a variation in total stress applied to the innercircumferential surface of the innermost metal ring, and a solid lineindicates a variation in total stress applied to the innercircumferential surfaces of the other metal rings. As can be seen fromFIG. 9, the middle value σm₁ of the stress on the innermost metal ringand the middle value σm_(n) of the stress on the other metal rings areequal to each other, but the amplitude σa₁ of the stress on theinnermost metal ring is larger than the amplitude σa_(n) of the stresson the other metal rings. A deviation between the amplitudes σa₁ andσa_(n) of both the stresses is due to the deviation between the amountΔσT₁ of variation in stress on the innermost metal ring and the amountΔσT_(n) of variation in stress on the other metal rings described withreference to FIG. 7.

As a result, the fatigue life of the innermost metal ring is shorterthan those of the other metal rings, and there is an increasedpossibility that the life of the metal belt may come to an end due tothe breakage of the innermost metal ring. Therefore, if the middleamplitude value σm₁ of the innermost metal ring approaches 0 (zero) asshown by a fine dashed line in FIG. 9, the deviation between the maximumvalue of the tensile stress and the maximum value of the compressivestress is decreased and hence, the fatigue life of the innermost metalring is prolonged to approach or accord with the fatigue life of theother metal rings, whereby the life of the entire metal belt can beprolonged. The middle amplitude value σm₁ of the innermost metal ring isdeviated toward the tension side from 0 (zero). For this reason, if acompressive residual stress is applied to at least the innercircumferential surface of the innermost metal ring, the middle valueσm₁ of the stress on the innermost metal ring can be brought close to 0(zero).

FIG. 10 is a graph with the middle value σm of stress taken on the axisof abscissa and the stress amplitude σa taken on the axis of ordinate.In FIG. 10, each of points on the same equi-life line indicates acombination of the middle value am of stress and the amplitude σa ofstress in which the fatigue lives are equal to each other. A point P₁ onan equi-life line L corresponds to the stressed state of the innermostmetal ring, and a point P_(n) on an equi-life line L′ corresponds to thestressed state of the other metal rings. The innermost metal ring shownby P₁ has the fatigue life which is smaller by a degree corresponding tothat the stress amplitude σa₁ thereof is larger than the stressamplitude σa_(n) of the other metal rings. At this time, if the middlevalue of the stress on the innermost metal ring is decreased from σm₁toward 0 (zero) to become equal to σm₁′, the stressed state P₁ of theinnermost metal ring is moved from the equi-life line L to a point P₁′on the equi-life line L′ of the other metal rings. As a result, all ofthe twelve metal rings ride on the same equi-life line L′, whereby thefatigue lives thereof are equal to one another and thus, the durabilityof the entire metal belt is enhanced.

If the middle value of the stress on the innermost metal ring isdecreased from σm₁ to 0, the stressed state P₁ of the innermost metalring is moved from the equi-life line L to a point P₁″ on an equi-lifeline L″ with a further larger fatigue life. As a result, the fatiguelife of the innermost metal ring is further prolonged. At the same time,if the middle value of the stress on the other metal rings is decreasedfrom σm_(n) toward 0, whereby the other metal ring is allowed to ride onthe equi-life line L″, the durability of the entire metal belt can befurther effectively enhanced.

To decrease the middle values σm₁ and σm_(n) of the stress on the metalrings, the compressive residual stress may be applied to at least theinner circumferential surface of the metal ring. An example of aparticular measure for applying the compressive residual stress is amethod of bombarding very small particles to the surface of the metalring by a shot blast or a water jet. Especially, if glass spheres havinga small diameter are mixed to water when the water jet is provided, thecompressive residual stress can be applied to the metal ring withoutcreation of a gash in the surface of the metal ring by fracturing theglass spheres by the shock of the bombardment.

Although the embodiment of the present invention has been described indetail, it will be understood that the present invention is not limitedto the above-described embodiment, and various modifications in designmay be made without departing from the subject matter of the inventiondefined by the claims.

For example, another measure such as a rolling and a thermal treatmentmay be used as the measure for applying the compressive residual stressto the metal ring. In addition, as is disclosed in Japanese PatentApplication Laid-open No. 2-154834, a method of spraying fluid which isobtained by mixing breakage-resistant particles and liquid together mayalso be employed as the method of applying the compressive residualstress to the metal ring.

What is claimed is:
 1. A belt for a continuously variable transmission,comprising a large number of metal elements carried on metal ringassemblies each of which is comprised of a plurality of endless metalrings laminated one on another, wherein a compressive residual stress isapplied to at least an inner circumferential surface of an innermost oneof the metal rings which is in contact with a saddle surface of themetal element, said compressive residual stress applied to the innermostmetal ring being larger than a compressive residual stress applied tothe metal rings other than the innermost metal ring.
 2. A belt for acontinuously variable transmission according to claim 1, wherein saidcompressive residual stress is applied to at least the innercircumferential surface of the innermost metal ring, so that a fatiguelife defined by an amplitude σa₁ and a middle value σm₁ of a stress onthe inner circumferential surface of the innermost metal ring is equalto a fatigue life defined by an amplitude σa_(n) and a middle valueσm_(n) of a stress on the inner circumferential surfaces of the metalrings other than the innermost metal ring.